It is well known that if a crystal structure has no inversion symmetry, it
may allow for Dzyaloshinskii-Moriya magnetic interactions, operating between
different crystallographic unit cells, which in turn should lead to the
formation of long-periodic spin-spiral structures. Such a behavior is
anticipated for two simple perovskites PbVO3 and BiCoO3, crystallizing in the
noncentrosymmetric tetragonal P4mm structure. Nevertheless, we argue that in
reality PbVO3 and BiCoO3 should behave very differently. Due to the fundamental
Kramers degeneracy for the odd-electron systems, PbVO3 has no single-ion
anisotropy. Therefore, the ground state of PbVO3 will be indeed the spin spiral
with the period of about one hundred unit cells. However, the even-electron
BiCoO3 has a large single-ion anisotropy, which locks this system in the
collinear easy-axis C-type antiferromagnetic ground state. Our theoretical
analysis is based on the low-energy model, derived from the first-principles
electronic structure calculations.Comment: 16 pages, 7 figures, 3 table